WO2002095650A2 - Method for determination of co-occurences of attributes - Google Patents
Method for determination of co-occurences of attributes Download PDFInfo
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- WO2002095650A2 WO2002095650A2 PCT/CA2002/000731 CA0200731W WO02095650A2 WO 2002095650 A2 WO2002095650 A2 WO 2002095650A2 CA 0200731 W CA0200731 W CA 0200731W WO 02095650 A2 WO02095650 A2 WO 02095650A2
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Definitions
- the invention relates to methods and apparatuses for determining co-occurences of attributes in objects. It also relates to attributes including biological response.
- One formulation ofthe general problem which encompasses many diverse applications, and which facilitates understanding ofthe principles described herein is a matrix of discrete features in which rows correspond to "objects" (such as diseases, individual patients, stock prices, consumers, or protein sequences) and the columns correspond to features, or attributes, or variables (such as drug sensitivity, gene expression, lifestyle factors, stocks, sales items, or amino acid residue positions).
- objects such as diseases, individual patients, stock prices, consumers, or protein sequences
- features, or attributes, or variables such as drug sensitivity, gene expression, lifestyle factors, stocks, sales items, or amino acid residue positions.
- a base method for identifying one or more characterizing attributes for an object that are likely to co-occur with one or more attributes of interest for the object comprises the steps of selecting one or more attribute sets of one or more characterizing attributes ofthe object, selecting an attribute set of one or more attributes of interest for the object, assigning a likelihood for each characterized attribute set that the attribute set occurs for the object when the attribute set of interest occurs for the object (each likelihood determined using one or more Bayesian computable classifiers on a dataset of attributes for a plurality of actual samples ofthe object), comparing each assigned likelihood against one or more likelihood thresholds, and reporting the assigned likelihoods ofthe characterizing attribute set based on the likelihood thresholds.
- the invention provides, a method comprising the steps of, selecting one characterizing attribute set of one or more attributes for the object, selecting an attribute of interest for the object, assigning a likelihood for the characterized attribute set that the attribute occurs for the object when the attribute of interest occurs for the object (the assigned likelihood determined using a Bayesian computable classifier on a dataset of attributes for a plurality of actual samples ofthe object), comparing the assigned likelihood against a likelihood threshold, and reporting the assigned likelihood ofthe characterizing attribute set based on the likelihood threshold.
- the invention provides, a method comprising the steps of, selecting one or more attribute sets of one or more characterizing attributes ofthe object, selecting an attribute set of one or more attributes of interest for the object, assigning a likelihood for each characterized attribute set that the attribute set occurs for the object when the attribute set of interest occurs for the object (each likelihood determined using one or more Bayesian computable classifiers on a dataset of attributes for a plurality of actual samples ofthe object), determining a likelihood significance for each assigned likelihood using artificial samples, and ranking the assigned likelihoods ofthe characterizing attribute set using the likelihood significance.
- the invention provides, a method comprising the steps of accessing one ofthe systems described below.
- a base system used to identify one or more characterizing attributes for an object that are likely to co-occur with one or more attributes of interest for the object using a dataset of samples of attributes for the object.
- the system comprises a computing platform, and a computer program on a computer readable medium for use on the computer platform in association with the dataset.
- the computer program comprises instructions to identify a characterizing attribute for an object that is likely to co-occur with an attribute of interest for the object, by carrying out the steps of one ofthe base methods.
- the methods may be used for drug discovery by identifying characterizing attribute sets for interaction by the drug using the steps one ofthe base methods for drug sensitive attributes of interest drug, and performing screens for drugs where growth in cells having desirably ranked characterizing attribute sets is drug sensitive.
- the methods may be used for identifying markers for diagnostic kits used to determine if a treatment is appropriate for a patient, by identifying a gene expression level set to be tested for in the patient by carrying out the steps of one ofthe base methods.
- the methods may be used for identifying markers for diagnosis of a living system by identifying an attribute set to be tested for in the living system using the steps of one of the base methods.
- the methods may also be used for identifying markers for prognosis of a living system by identifying an attribute set to be tested for in the living system using the steps of one ofthe base methods.
- the diagnosis or prognosis may be with . respect to a disease or syndrome type of a patient.
- the methods may also be used for identifying markers for determing the appropriateness of a therapy or treatment of a living system by identifying an attribute set to be tested for in the living system using the steps of one ofthe base methods.
- the attributes ofthe attribute set may include protein concentrations.
- the protein concentrations may include tissue protein concentrations.
- the protein concentrations may include serum protein concentrations.
- the attributes ofthe attribute set may include molecular markers.
- the molecular markers may include blood molecular markers.
- the molecular markers may include tissue molecular markers.
- the attributes ofthe attribute set may include clinical observables.
- the clinical observables may include microscopic clinical observables.
- the clinical observables may include macroscopic clinical observables.
- the markers may be for diagnostic kits used in the diagnosis, for diagnostic procedures used in the diagnosis, for prognostic kits used in the prognosis, or for prognostic procedures used in the prognosis.
- a likelihood threshold for each characterizing attribute set may be determined using the same Bayesian classifiers as the assigned likelihood on a dataset of attributes for a plurality of artificial samples ofthe object.
- a likelihood threshold for each characterizing attribute set may be determined by computing those characterizing attribute sets with an assigned likelihood above a given percentile of all assigned likelihoods for the relevant attribute set.
- Artificial samples may be created by randomizing the actual gene expression levels for the characterizing attributes. Artificial samples may be created by transposing the actual gene expression levels for each characterizing attribute to another characterizing attribute.
- the assigned likelihoods ofthe characterizing attribute sets may be compared against a likelihood threshold determined by computing those characterizing attribute sets with an assigned likelihood above a given percentile of all assigned likelihoods for the relevant attribute set of interest.
- the characterizing attributes may be gene expression levels and the attribute of interest may be drug sensitivity level, drug dose (absolute concentration or dose relative to some standard dose) along an increasing or decreasing scale, dose of drug which causes half- maximal cellular growth rate, or -logarithm 10 (dose) where dose is the dose which yields half-maximal total cell mass accumulating under otherwise standard conditions.
- Drug sensitivity level may represent growth inhibiting in diseased cells, a lack of growth inhibiting in diseased cells, patient toxicity in healthy cells.
- the attributes may be represented in a dataset taken from the NCI60 dataset.
- the Bayesian classifier may be selected from a group consisting of linear discriminant analysis, quadratic discriminant analysis, and a uniform gaussian analysis.
- the characterizing attribute sets ranked following comparison ofthe likelihood and the likelihood threshold may be reported.
- the ranked characterizing attributes sets may be reported to one of a group consisting of a computer readable file stored on computer readable media, a printed report, and a computer network.
- the assigned likelihoods may be ranked by assigned likelihood and subranked by likelihood significance.
- the assigned likelihood may be compared against a likelihood threshold, and the assigned likelihood ofthe characterizing attribute set may be reported based on the likelihood threshold and the ranking ofthe assigned likelihood.
- FIG. 1 is a first Venn diagram of statistically significant results of analyses employed in the preferred embodiment ofthe invention.
- FIG. 2 is a second Venn diagram of statistically significant results of analyses employed in the preferred embodiment of the invention
- FIG. 3 is a plot of results from a 2D QDA analysis of a dataset according to the preferred embodiment ofthe invention
- FIG. 4 is a plot of results from a 2D LDA analysis of a dataset according to the preferred embodiment ofthe invention
- FIG. 5 is a plot of results from a 2D QDA analysis of a dataset according to the preferred embodiment ofthe invention
- FIG. 6 is a plot of results from a 2D UGDA analysis of a dataset according to the preferred embodiment ofthe invention.
- FIG. 7 is a plot of results from a ID LDA analysis of a dataset according to the preferred embodiment of the invention.
- FIG. 8 is a plot of results from a ID UGDA analysis of a dataset according to the preferred embodiment ofthe invention.
- FIG. 9 is an example flow chart of a computer program according to the preferred embodiment ofthe invention.
- FIG. 10 is an example block diagram of a system according to the preferred embodiment ofthe invention.
- FIG. 11 is an example flow chart of a computer program according to an alternate embodiment ofthe invention.
- FIG. 12 is an example block diagram of a system according to an alternate embodiment ofthe invention.
- FIG. 13 is an example flow chart of a computer program according to an alternate embodiment ofthe invention.
- FIG. 14 is an example block diagram of a system according to an alternate embodiment ofthe invention
- FIG. 15 is an example flow chart of a computer program according to an alternate embodiment ofthe invention.
- FIG. 16 is an example block diagram of a system according to an alternate embodiment ofthe invention. MODES FOR CARRYINGOUTTHE INVENTION
- a base method identifies one or more characterizing attributes for an object that are likely to co-occur with one or more attributes of interest for the object.
- the method comprises the steps of selecting one or more attribute sets of one or more characterizing attributes ofthe object, selecting an attribute set of one or more attributes of interest for the object, assigning a likelihood for each characterized attribute set that the attribute set occurs for the object when the attribute set of interest occurs for the object (each likelihood determined using one or more Bayesian computable classifiers on a dataset of attributes for a plurality of actual samples ofthe object), comparing each assigned likelihood against one or more likelihood thresholds, and reporting the assigned likelihoods ofthe characterizing attribute set based on the likelihood thresholds.
- the method comprises the steps of, selecting one characterizing attribute set of one or more attributes for the object, selecting an attribute of interest for the object, assigning a likelihood for the characterized attribute set that the attribute occurs for the object when the attribute of interest occurs for the object (the assigned likelihood determined using a Bayesian computable classifier on a dataset of attributes for a plurality of actual samples ofthe object), comparing the assigned likelihood against a likelihood threshold, and
- the method comprises the steps of, selecting one or more attribute sets of one or more characterizing attributes ofthe object, selecting an attribute set of one or more attributes of interest for the object, assigning a likelihood for each characterized attribute set that the attribute set occurs for the object when the attribute set of interest occurs for the object (each likelihood determined using one or more Bayesian computable classifiers on a dataset of attributes for a plurality of actual samples ofthe object), determining a likelihood significance for each assigned likelihood using artificial samples, and ranking the assigned likelihoods ofthe characterizing attribute set using the likelihood significance.
- the method comprises the steps of accessing one of the systems described below.
- a base system is used to identify one or more characterizing attributes for an object that are likely to co-occur with one or more attributes of interest for the object using a dataset of samples of attributes for the object.
- the system comprises a computing platform, and a computer program on a computer readable medium for use on the computer platform in association with the dataset.
- the computer program comprises instructions to identify a characterizing attribute for an object that is likely to co-occur with an attribute of interest for the object, by carrying out the steps of one ofthe base methods.
- the base methods can be used for drug discovery by identifying characterizing attribute sets for interaction by the drug using the steps one ofthe base methods for drug sensitive attributes of interest drug, and performing screens for drugs where growth in cells having desirably ranked characterizing attribute sets is drug sensitive.
- the base methods can be used for identifying markers for diagnostic kits used to determine if a treatment is appropriate for a patient, by identifying a gene expression level set to be tested for in the patient by carrying out the steps of one ofthe base methods.
- a likelihood threshold for each characterizing attribute set can be determined using the same Bayesian classifiers as the assigned likelihood on a dataset of attributes for a plurality of artificial samples ofthe object.
- a likelihood threshold for each characterizing attribute set can be determined by computing those characterizing attribute sets with an assigned likelihood above a given percentile of all assigned likelihoods for the relevant attribute set.
- the characterizing attributes may be gene expression levels and the attribute of interest may be drug sensitivity level, drug dose (absolute concentration or dose relative to some standard dose) along an increasing or decreasing scale, dose of drug which causes half-maximal cellular growth rate, or - logarithm 10 (dose) where dose is the dose which yields half-maximal total cell mass accumulating under otherwise standard conditions.
- Drug sensitivity level may represent growth inhibiting in diseased cells, a lack of growth inhibiting in diseased cells, patient toxicity in healthy cells.
- the attributes may be represented in a dataset taken from the NCI60 dataset.
- the Bayesian classifier may be selected from a group consisting of linear discriminant analysis, quadratic discriminant analysis, and a uniform/gaussian analysis.
- the characterizing attribute sets ranked following comparison ofthe likelihood and the likelihood threshold may be reported.
- the ranked characterizing attributes sets may be reported to one of a group consisting of a computer readable file stored on computer readable media, a printed report, and a computer network.
- the assigned likelihoods may be ranked by assigned likelihood and subranked by likelihood significance.
- the assigned likelihood may be compared against a likelihood threshold, and the assigned likelihood ofthe characterizing attribute set may be reported based on the likelihood threshold and the ranking ofthe assigned likelihood.
- the objects may be a particular disease, while the samples are taken from different patients and the attributes are particular expression levels of particular genes and sensitivity to a particular drug.
- the samples may be cells. Using the data in Table 1, sample 1 from a cell having disease A is taken from a first patient. The disease A cell from the patient has sensitivity to drug I and gene expression levels d, e, f. Similarly, sample 2 from a cell having disease B may also be taken from the same patient. The disease B cell from the patient has sensitivity to drug II and gene expression levels d, g, h. Sample 3 from a cell having disease A is taken from a different patient. The disease A cell from the patient has sensitivity to drug I and gene expression levels d, h.
- drag I is an attribute set of interest and gene expression levels d and e are a characterizing attribute set. This may be represented in a matrix in the form of Table 2.
- object A and object B may be part of a generic object C.
- object C For example, one may be interested in knowing if a number of forms of cancer are sensitive to the same drag. In this case, the relevant samples may change.
- the first patient has two forms of cancer A and B. If one is looking for drag sensitivity in both cancers A and B then the all the samples may be relevant, while the object is cancers of type A and B. This permits the use of samples from the same patient for different cancers. Samples from the same patient with the same attribute of interest would ordinarily be considered to be only one sample.
- the particular definition of objects, samples, attributes of interest and characterizing attributes is a matter of choice for the designer of a particular embodiment. It is recognized that some choices may be superior to others; however, that does not bring them any of them outside ofthe principles described herein.
- the datasets may contain many different samples, some of which will not contain attribute sets of interest for a given run ofthe methods. These can be filtered out before the methods are run, or they may be left in the dataset to be accessed when the methods are ran.
- Each ofthe features for an object may be numerical or qualitative.
- the features are transformed into ordinal (values capable of being ordered) variables, termed attributes.
- the principles described herein can be extended to attributes sets of interest and characterizing sets of higher orders. For example, one may want to know if sensitivity to a particular cocktail of drags co-occurs with a particular combination of gene expression levels.
- Attributes may not simply be a part of an object, such as its gene expression levels, but may be factors or things that could broadly be related to the object, such as weather on a particular day (attribute) may be related to the price (attribute) of an agricultural stock (object). It is also understood that objects are not limited to traditionally tangible objects, but may be intangible objects such as bonds or stocks as well.
- characterizing attribute set that is likely to co-occur with an attribute set of interest does not necessarily imply that the characterizing attribute set is causing the attribute of interest; however, in many situations this information continues to be useful.
- symptoms may act as a useful disease marker (attribute of interest); however, they are caused by, and do not generally cause, the disease.
- the methods can form part of methods for identifying possible drug targets. Once it is known that a disease or diseased cell is affected by drags that appear to interact with cells having particular combinations of gene expression levels then screening studies can be conducted to find other drags that also inhibit growth in cells with those combinations of expression levels.
- the base method takes a dataset of samples of objects, including a characterizing attributes set and an attribute set of interest, as input.
- the method generates an output display of characterizing attribute sets that have a substantial likelihood of co-occurring with the attribute set of interest.
- one or more characterizing attribute sets are selected, and one or more attribute sets of interest are selected.
- the likelihood of each characterizing attribute set co-occurring in actual samples ofthe object is determined using a Bayesian computable classifier.
- a likelihood of each characterizing set occurring in artificial samples is used to determine a likelihood threshold. Only those characterizing attribute sets with a likelihood co-occurrence greater than its likelihood threshold is selected.
- an embodiment ofthe method may take a collection of biological samples, their gene expression measurements (characterizing attributes), and a binary high low drug response measurement (attributes of interest) as input.
- the method generates a prioritized list of genes, ranked by their p- values or ability to correctly predict the drug response (likelihood of co-occurrence).
- the method consists of three steps:
- Step 1) can take a number of forms.
- a simple list of all single genes can be a collection of (singleton) gene sets.
- a list of all pairs of genes can be a collection of (gene pair) candidate gene sets.
- Pre-processing techniques such as those described in PCT Patent Application PCT/CA98/00273 filed March 23 1998 under title Coincidence Detection Method, Products and Apparatus, inventor Evan W. Steeg, published October 1 1998 as WO 98/43182 may be used to create candidate gene sets.
- Alternative pre-processing techniques may be used, including by way of example, standard feature detectors, or known gene pathway tables.
- Step 2) can also take a number of forms.
- Classical statistical techniques such as Linear Discriminant Analysis or Quadratic Discriminant Analysis can be used.
- Other probabilistic models such as the Gaussian/Uniform, can be tailored to particular applications or to suit biological intuition.
- Step 3) involves the comparison ofthe classification scores from step 2) to those generated from randomized data.
- Multiple datasets (on the order of 100 or more) are generated by permuting the gene expression values over the samples, i.e. if samples were rows and genes were columns in a table, we would permute the entries in each column, independently.
- Steps 1) and 2) are repeated for the randomized data, and the scores from the real data are compared to the scores from the randomized data.
- the scores are ranked according to those most likely to indicate a cooccurrence and those scores greater than the scores for randomized data. Selections can be made according to the rank ofthe scores for the non-randomized data, or according to the rank ofthe difference ofthe scores for the real and randomized data. Selections may also be based on other calculations using the real and random scores.
- validation can be determined either by comparing classification scores from the real data to all the classification scores from the randomized data and then applying the Bonferroni correction, or by comparing the most extreme classification accuracies from each randomized trial to the most extreme classification accuracy from the real data.
- An empirical p-value can be obtained directly by calculating the proportion of random datasets for which their extreme classification accuracies exceeded that in the real data. Only those gene sets with p- values below a user-selected cutoff are reported.
- Drag sensitivities were reported as -logGI50 s, with the log being base 10. All the drag sensitivities were normalized to mean zero so that the measurement really reflected differential growth inhibition. We wanted to categorize the cell line response into “uninhibited” and “inhibited”, with a small gray area to avoid the effects of harsh cutoffs. In that scale, a value of 1.0 for a cell line/drag combination meant that the cell line was inhibited to 50% growth at 1/10 the dosage ofthe "average” drug. For our purposes, we wanted to identify those drags that were effective at least 1/5 the "average" dosage, which in the log scale turns into 0.7.
- Sensitivities in the range [0.7,1] are partially in both classes. Since it varies between 0 and 1 , the function f can be viewed as a fuzzy classification or a probability.
- f(r) Probability of sensitivity in high class
- l-f(r) Probability of sensitivity in low class.
- LDA Lightly modified to account for partial class membership
- Lexpr expression of gene A in cell line L
- Lsensitivity sensitivity of cell line L to drag B
- ID discriminants we also used 2 other methods similar to LDA, to search for correlations between sensitivity and gene expression
- QDA differs from LDA in that the original variances of Gh and Gl are used in Equation 1, instead ofthe average ofthe variances as a result, QDA can have nonlinear decision boundaries between classes while LDA has linear decision boundaries.
- MSE scores The statistical significance of MSE scores was determined by comparing against results from randomized data. Statistical significance was adjusted by the Bonferroni method to account for multiple tests, (i.e. for a given drag the statistical significance of a score from a ID discriminant was multiplied by 1000; statistical significance of scores from 2D discriminants was multiplied by 10 A 5).
- LDA linear discriminant analysis
- QDA quadratic discriminant analysis
- Bayesian model a uniform/Gaussian discriminant
- LDA ID linear ID methods
- Nonlinear methods therefore identify gene-drag associations not found by a linear method. This is the case for both 1 -dimensional (ID) analysis involving correlations between a single gene and one drug, and for 2D analysis involving correlations between pairs of genes and one drug (gene, gene, drug triples).
- ID 1 -dimensional
- 2D analysis involving correlations between pairs of genes and one drug (gene, gene, drug triples).
- LDA ID yielded only five gene markers not identified by at least one of the other methods.
- QDA ID 1 gene was found by this method only.
- Uniform gaussian ID was the most effective ofthe ID methods in this respect, yielding 9 genes correlated with high sensitivity found by this method only.
- genes peculiar to each 2D method included (in pair combinations) 52 genes for LDA, 32 genes for QDA, and 49 genes for uniform/Gaussian.
- FIG. 3 An example ofthe 2D approach is diagrammed in Fig. 3.
- Expression levels ofthe gene elongation factor TU are plotted vs. expression levels ofthe gene SID W 116819 for the 60 cell lines, whose sensitivities to fluorodopan varied.
- the areas mapped out by the Gaussian distributions separate most ofthe black (filled-in squares) points (highly sensitive) cell lines from the white (open squares) points (low sensitivity) cell lines, placing them in separate regions ofthe graph. Twelve cell lines with high sensitivity to fluorodopan (black points) had varying levels of expression for both genes 1 and 2.
- Fig. 3 Expression levels ofthe gene elongation factor TU are plotted vs. expression levels ofthe gene SID W 116819 for the 60 cell lines, whose sensitivities to fluorodopan varied.
- the areas mapped out by the Gaussian distributions separate most ofthe black (filled-in squares) points (highly sensitive) cell lines from the white (open
- Figs. 3 through 6 depict 2D analysis of gene expression-drag sensitivity data for 60 cancer cell lines.
- Fig. 3 employs QDA analysis.
- Each point represents a cell line, with its location specified by the relative expression of two genes (x and y coordinates).
- the points are coloured by the cell line's response to Fluorodopan.
- the contours represent points of equal probability as predicted by the methods described herein. In general the areas where black squares tend to be concentrated are areas of predicted high sensitivity.
- the arrows indicate the direction of predicted increasing sensitivity.
- the outermost contour to the bottom left and top right show the decision surface generated by the two Gaussian distributions: outside the outermost contour are classified as high response and the between the gradients as low response.
- both SID W 242844 and SID W 26677 are needed to predict high sensitivity to mitozolamide.
- (+) is associated with low sensitivity only, while (-) can be associated with low or high sensitivity.
- (+) is always associated with low, and (+) can correspond to either high or low sensitivity.
- the combination (- +) corresponds to high sensitivity only, so both genes are needed to establish a correlation with high sensitivity.
- Table 5
- both SID W 242844 and ZFP36 are needed to predict high sensitivity to mitozolamide.
- SID W 242844 (-) can correspond to either high or low sensitivity, and (+) corresponds to low sensitivity.
- (+) corresponds to low sensitivity.
- ZFP36 (-) corresponds to either high or low, and (+) corresponds only to low sensitivity.
- the combination (- -) corresponds only to high sensitivity, so both genes are needed for the correlation.
- this range of values includes zero (no deviation in expression from mixed culture control). This is acceptable, since we are interested only in relative basal gene expression levels, not perturbed gene expression relative to the control. For example, a combination of approximately zero (0) expression for gene SID 289361 and positive (+) expression for gene SID 327435 correlated with high sensitivity to fluorouracil according to QDA 2D, in one case.
- Figs. 7 and 8 The ID approach is shown in Figs. 7 and 8. For single gene correlations, only the value on the x-axis (horizontal axis) is considered. A random variable was used to create a y- axis (vertical axis) as a visual aid to avoid the problem of overlapping points.
- Fig. 7 according to LDA ID, cell lines with high sensitivity to mitozolamide exhibited high levels of PTN expression.
- Fig. 8 Uniform/gaussian ID determined that cells with high sensitivity to mitozolamide expressed DOC-2 mitogen- responsive phosphoprotein in a particular range of values above control. Random variable on y-axis permits visualization of data points that would obscure one another in a one-dimensional graph.
- Markers identified by these computational methods could be used as the basis for diagnostic tests specific for those genes, perhaps in the form of smaller-scale microarray assays. Tests such as these would be aimed directly toward determination ofthe best choice(s) for therapeutic drag treatment. For example, a diagnostic test indicating high expression levels for both genes elongation factor TU and SID W 116819 (Fig. 3) would suggest a high probability of a response to fluorodopan treatment.
- the present study focused on basal gene expression patterns as indicators of drag sensitivity.
- we computationally distinguish strong from weak biological responses i.e., to discriminate, classify, or predict biological responses.
- the method employs computationally-derived associations between computationally-analyzed quantitative gene expression data and computationally-analyzed quantitative intensity data.
- the intensity data represents observables (other than gene expression) assumed to be related in some arbitrary, but graded, manner to the biological responses.
- f — 1 is interpreted to mean "very substantial, strong, or high biological response"
- the domain U of f is defined to be a 1 -parameter continuous path in m- dimensional space.
- U can simply be scalar, i.e., U c R l ; or U can be an arbitrary 1-parameter path through higher-dimensional space R m , m > l (e.g., a series of m- dimensional feature vectors indexed by continuous time).
- the examples provided here concentrate on the scalar domain case (i.e., U c R 1 ), but the approach also applies to cases of higher-dimensional continuous 1-parameter paths.
- Domain U cz R 1 is interpreted to mean:
- U represents drag dose (absolute concentration or dose relative to some standard dose) along an increasing, or decreasing, scale
- U can represent the dose of drag which causes half-maximal cellular growth rate as charted along a scale which decreases to the right;
- GI50 drag dose which yields 50% ofthe cellular mass which is achieved under some standard untreated-with-drug conditions. Note that in this last example, r increases as GI50 decreases. In this case, an increasing r represents a decreasing "intensity of dose needed to obtain some defined biological effect.”
- the function f assigns a readily interpretable numerical "biological response score" in the continuous interval [0, 1 ] to a "degree or intensity of external effect on biology” from a scale U ⁇ z R l .
- f is what inexorably links "intensity of external effect on biology” to a readily interpreted biological response scale, where the interpretations of f values are given in la) above.
- i denote, or label, any given external effect, or situation, on the biology, e.g., temperature, pH, therapeutic intervention, compound applied, drug dosed, etc. (For explanatory convenience, for now on we often refer to any external effect on the biology as "drug.")
- k denote, or label, any given gene, mRNA species, gene product, or protein. (For explanatory convenience, for now on we often refer to any of these entities as "gene.”)
- g denote, or label, gene abundance or expression level, however numerically adjusted or normalized, of gene k in cell line .
- a represent, or label, any desired categorical description of biological response score.
- w represent, or label, generally the biological response score (i.e., f value) of any biological source under any external effect or situation, e.g., the sensitivity of a cell line to a drag.
- w' ,J specifically denote, or label, the biological response score (i.e., f value) of biological source / * under any external effect or situation i , e.g., f value of cell line under some specified exposure to drug i .
- HY specifically denote, or label, the biological response score (i.e., f value) which falls in some particular category a (e.g., a - sensitive) of biological source / under any external effect or situation i , e.g., w;' e J nsitlve means the f value is 1 for cell line under some specified exposure to drug i .
- a e.g., a - sensitive
- C a ' denote the set of biological sources falling in biological response category a when the biological source is external effect i .
- C s ' ensitive is the set comprising cell lines for which the respective f values are 1 when exposed to drag i at some specified dose, i.e., the set of cell lines sensitive to drag / .
- C' denote the cardinality of C a ' , i.e., the number of elements in set C a ' .
- Compute histogram comprising g , for given k , for e C' .
- ⁇ g the square root of the average variance.
- Compute discriminators, classifiers, and predictors of a the category- wise biological response to external event i , but based on information computed from a given gene k .
- fi (si) probability of abundance value g k ' from the gaussian density fitted to the histogram ofthe gene k abundances over the cell lines in response category a when subjected to biological effect .
- a probability difference for the above probability is also computed, e.g.,
- differ ence Bayesim is the difference between 'the predicted probability that cell line is in the category a as computed from the gene k abundances across cell lines ' and 'the Observed probability that cell line / is in category a as computed from the effects of biological effect i on the cell lines'.
- This method computes a Bayesian conditional probability P(j e c? e " s '" ve
- the probability is computed using the following equation: fisensitive s j _ p, ⁇ sensitive
- P(j e Cr llve ⁇ gi) - G sensitive j ⁇ ns / ⁇ sensitive ⁇ , 7 - 7 - / admir. i ⁇ rjs ⁇ insensitive ⁇ , k (g k ) - P( c i ) +i u ⁇ gk) - ( c i )
- ⁇ k n standard deviation of gene k abundances in the sensitive cell lines
- Paclitaxel Taxol
- This method computes a Bayesian conditional probability P(j e C* e ' mt ⁇ ve ⁇ g k J ,gj) that a cell line j is sensitive to drug i , given the abundances of two genes k and
- i G k l' sitive (g ⁇ , gj ) joint probability of abundance values gl and gj from the bivariate gaussian density fitted to the histogram of gene k and / abundances over the sensitive cell lines when subjected to drag i .
- ⁇ k n standard deviation of gene k abundances in the sensitive cell lines
- Gene 1 Human putative 32kDa heart protein PHP32 mRNA complete cds Chr.8 [417819 (EW) 5*:W88869 3':W88662]
- Gene 2 SID W 305455 TRANSCRIPTIONAL REGULATOR ISGF3 GAMMA SUBUNIT [5':W39053 3':N89796]
- Gene 2 Homo sapiens mRNA for KIAA0638 protein partial cds Chr.l 1 [470670 (IW)
- Gen L ⁇ e 1 *Homo sapiens lysosomal neuraminidase precursor mRNA complete cds SID
- This method computes a Bayesian conditional probability P( J i s ' sensitive I [ S 2 kJ
- ⁇ k n mean of gene k abundances in the sensitive cell lines
- avg k sensitive ⁇ insensitive class-weighted average standard deviation of gene k abundances in the sensitive cell lines
- This method computes a Bayesian conditional probability P( KJ i e c > sensitive I s ⁇ - k/ ) J that a cell line J is sensitive to drag z , given the gene k abundance ? k in cell line J .
- the probability is computed using the following equation: .
- This method computes a Bayesian conditional probability that a cell line ⁇ is sensitive to drag z , given the abundances of genes k and 1, gk J ⁇ ⁇ respectively, in cell line J .
- ⁇ k " mean of gene k abundances over the sensitive cell lines
- avg k sensitive ⁇ insensitive class-weighted average standard deviation of gene k abundances in the sensitive and insensitive cell lines
- Gene 1 SID W 254085 ESTs Moderately similar to synaptonemal complex protein [M.musculus] [50N71532 30N22165] Gene 2: SID 118593 [5':T92821 30T92741]
- Gene 1 XRCC4 DNA repair protein XRCC4 Chr.5 [26811 (RW) 50R14O27 30R39148]
- Gene 2 SID W 242844 ESTs Moderately similar to ! ! ! ! ALU SUBFAMILY J WARNING ENTRY !!! [H.sapiens] [50H94138 30H94O64]
- Gene 1 SID 260048 Homo sapiens intermediate conductance calcium-activated potassium channel (hKCa4) mRNA complete [5': 30N32O1O]
- Gene 2 SID W 487535 Human mRNA for KIAA0080 gene partial cds [50AAO43528 30AAO43529]
- Gene 1 SID W 510534 MAJOR GASTROINTESTINAL TUMOR-ASSOCIATED PROTEIN GA733-2 PRECURSOR [5':AA055858 3':AA055808] Gene 2: SID W 242844 ESTs Moderately similar to ! ! ! ! ALU SUBFAMILY J WARNING ENTRY !
- Gene 1 X-ray induction of mdm2-log Gene 2: Human thymosin beta-4 mRNA complete cds Chr.20 [305890 (IW) 5':W19923 30N91268]
- Gene 1 SID W 345683 ESTs Highly similar to INTEGRAL MEMBRANE GLYCOPROTEIN GP210 PRECURSOR [Rattus norvegicus] [50W76432 30W72O39]
- Gene 2 Human clone 23933 mRNA sequence Chr.17 [23933 (IW) 50T77288 30R39465]
- Gene 1 SID W 489301 ESTs [50AAO54471 3':AA058511]
- Gene 2 H.sapiens mRNA for TRAMP protein Chr.8 [149355 (IEW) 5':H01598 3':H01495]
- Gene 1 GAMMA-INTERFERON-INDUCIBLE PROTEIN IP-30 PRECURSOR Chr.19 [310021 (I) 5': 3':N99151]
- Gene 2 Homo sapiens lysyl hydroxylase isoform 2 (PLOD2) mRNA complete cds Chr.3 [310449 (IW) 5':W30982 30N98463]
- Gene 1 ESTs Chr.19 [485804 (EW) 50AAO4O35O 30AAO4O351]
- Gene 1 SID W 358526 ESTs [50W96O39 30W94821]
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WO2005119564A3 (en) * | 2004-06-04 | 2006-03-02 | Bayer Healthcare Ag | Method for the use of density maps based on marker values in order to diagnose patients with diseases, particularly tumors |
JP2007526454A (en) * | 2004-01-28 | 2007-09-13 | アットー バイオサイエンス インコーポレイテッド | Interpolated image response |
DE102007005070A1 (en) | 2007-02-01 | 2008-08-07 | Klippel, Wolfgang, Dr. | Linear and non-linear parameters e.g. resistance, estimating arrangement for e.g. failure diagnoses of transducer, has nonlinear estimator with output that receives error free nonlinear parameter, even if estimation error occurs |
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2002
- 2002-05-17 WO PCT/CA2002/000731 patent/WO2002095650A2/en not_active Application Discontinuation
- 2002-05-17 AU AU2002302243A patent/AU2002302243A1/en not_active Abandoned
- 2002-05-17 US US10/478,418 patent/US20040158581A1/en not_active Abandoned
- 2002-05-17 CA CA002447857A patent/CA2447857A1/en not_active Abandoned
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US20040158581A1 (en) | 2004-08-12 |
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WO2002095650A3 (en) | 2003-10-30 |
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